My Gen IIs have spent many days riding in Scottish rain.
Scottish rain is different from rain anywhere else. Not necessarily heavier, but definitely wetter. It will find its way into anything that can possibly be affected by water (and anywhere else, even if it's not affected).
The guy who organised many of the trips I've done in Scotland was used by Gore for years to test Gore-tex suits, glove, boots. He normally rides FJRs, though currently on a time-out with broken ribs, nothing to do with motorcycles. Never had any problems with his FJRs, rain or shine (except for wearing tyres out).
The FJRs (and most motorcycles) are simply not affected. I exclude the Trophy I had, which did suffer from damp.
Worry about your comfort, your safety (car drivers are even more blind when it's raining), road conditions. Don't worry about the bike.